Next, we study the dipolar interaction and anisotropy axis orientation effect on the magnetic relaxation in a square assembly of MNPs. In Fig. (REF ), we plot \(M(t)/M^{}_s\)  versus \(t\)  curve with \(A^{}_r=1.0\)  for six typical values of \(\alpha =0, 30, 45, 60, 75\) , and \(90^\circ \) . We have also considered six representative values of \(h^{}_d=0.0\) , 0.2, 0.4, 0.6, 0.8, and 1.0. Irrespective of \(\alpha \) , the functional form of the magnetization-decay curve is perfectly exponentially decaying for weak dipolar interaction \(h^{}_d\le 0.3\) . There exists a transition point at \(h^{}_d\approx 0.4\) ; magnetization relaxes slowly for \(\alpha \le 45^\circ \) . While with \(\alpha >45^\circ \) , magnetization decays rapidly. Remarkably, there is a fastening in magnetization relaxation with large dipolar interaction strength (\(h^{}_d>0.4\) ) compared to weakly interacting MNPs. It can be attributed to enhanced antiferromagnetic coupling because of dipolar interaction in the square arrangement of MNPs. Interestingly, the relaxation characteristics depend very weakly on the orientation of anisotropy axes for a given interaction strength. It could be due to the symmetric nature of the system. Figueiredo et al.  also observed exponential decay of magnetization for weakly interacting MNPs [1]}. The observation of fastening of magnetic relaxation due to antiferromagnetic coupling induced by dipolar interaction is in perfect agreement with our recent work [2]}. We found characteristic magnetic hysteresis of antiferromagnetic dominance in a square arrangement of MNPs [2]}. De'Bell et al. also obtained the minimum energy state to be antiferromagnetic in the square array [4]}.
